Monoid Ring of Commutative Monoid over Commutative Ring is Commutative

Theorem

Let $R$ be a commutative ring.

Let $G$ be a commutative monoid.

Let $\sqbrk R G$ be the monoid ring of $G$ over $R$.

Then $\sqbrk R G$ is commutative.

Proof

This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.